Phenomenological Damping Research Articles

The spatial Whitham equation

The Whitham equation is a non-local, nonlinear partial differential equation that models the temporal evolution of spatial profiles of surface displacement of water waves. However, many laboratory and field measurements record time series at fixed spatial locations. To directly model data of this type, it is desirable to have equations that model the spatial evolution of time series. The spatial Whitham (sWhitham) equation, proposed as the spatial generalization of the Whitham equation, fills this need. In this paper, we study this equation and apply it to water-wave experiments on shallow and deep water. We compute periodic travelling-wave solutions to the sWhitham equation and examine their properties, including their stability. Results for small-amplitude solutions align with known results for the Whitham equation. This suggests that the systems are consistent in the weakly nonlinear regime. At larger amplitudes, there are some discrepancies. Notably, the sWhitham equation does not appear to admit cusped solutions of maximal wave height. In the second part, we compare predictions from the temporal and spatial Korteweg–de Vries and Whitham equations with measurements from laboratory experiments. We show that the sWhitham equation accurately models measurements of tsunami-like waves of depression, waves of elevation, and solitary waves on shallow water. Its predictions also compare favourably with experimental measurements of waves of depression and elevation on deep water. Accuracy is increased by adding a phenomenological damping term. Finally, we show that neither the sWhitham nor the temporal Whitham equation accurately models the evolution of wave packets on deep water.

Radio-frequency sheath excitation at the extremities of scrape-off layer plasma filaments, mediated by resonant high harmonic fast wave scattering

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

Stopping and image forces acting on a charged particle moving near a graphene- Al2O3 -graphene heterostructure

We study the impact of plasmon-phonon hybridization on the stopping and image forces acting on a charged particle moving parallel to a graphene-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$-graphene sandwichlike composite system by considering a broad domain in the parameter space. The effective dielectric function of the system is obtained using two descriptions of the electronic response of doped graphene: an ab initio method based on the time-dependent density functional theory calculations and an analytical expression based on the massless Dirac fermion (MDF) approximation for graphene $\ensuremath{\pi}$ bands. It is found that the main discrepancies between the two methods come from the high-energy interband electron transitions, which are included in the ab initio method but not in the MDF method. Special attention is paid to the regime of low-particle speeds, where the MDF method compares well with the ab initio method, but the modeling is sensitive to the effects of finite temperature and the treatment of phenomenological damping. It is observed at low particle speeds that both forces exhibit an interesting interplay between the hybrid modes of the phononic type and the continuum of the intraband electron-hole excitations in graphene. Furthermore, the effects of the lowest-energy antisymmetric modes, which exhibit acoustic dispersions at long wavelengths in a system with equally doped graphene layers, are exposed in calculations of the stopping force on a co-moving pair of incident particles with opposite charges that are symmetrically positioned around the target system.

Self-sensing active artificial hair cells inspired by the cochlear amplifier, Part I: Theoretical and numerical realization

The mammalian cochlear amplifier displays a unique nonlinear characteristic of amplifying or compressing the acoustic stimuli based on their level. Designing control algorithms for artificial hair cells (AHCs) with active sensing capabilities could mimic such dynamics. The present work focuses on developing a novel self-sensing active AHC scheme that implements the amplification/compression function of the AHCs and extends the authors’ previous designs for future cochlear implants or sensor design applications. The AHC functions near a Hopf bifurcation and varies the output piezoelectric voltage by a power-law relationship with the input. It is the first time that a self-sensing AHC is modeled as a quadmorph cantilever controlled by a phenomenological cubic damping controller. The AHC’s control signal is supplied to a pair of its piezoelectric layers and the output of the AHC is the sensed voltage of the second piezoelectric pair. This is in contrast to the previous studies where the AHC’s tip-velocity was measured with external sensors. The requirement of permanent external sensors in the system was a strict limitation that is eliminated in this work. An in-depth study of this novel AHC is conducted in this paper and AHC’s implementation is examined experimentally in Part II of the paper.

Turbulent Relaxation to Equilibrium in a Two-Dimensional Quantum Vortex Gas

We experimentally study emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the meanfield Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\cal{H}$ and angular momentum $\cal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\hat{\beta}$ and rotation frequency $\hat{\omega}$. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero-temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.

Energy balance and energy correction in dynamics of classical spin systems.

An energy-correction method is proposed as an addition to mainstream integrators for equations of motion of systems of classical spins. This solves the problem of nonconservation of energy in long computations and makes mainstream integrators competitive with symplectic integrators for spin systems that for different-site interactions conserve the energy explicitly. The proposed method is promising for spin systems with single-site interactions for which symplectic integrators do not conserve energy and thus have no edge against mainstream integrators. From the energy balance in the spin system with a phenomenological damping and Langevin fields, a formula for the dynamical spin temperature in the presence of single-site anisotropy is obtained.

Taming Faraday waves in binary fermionic clouds: The effect of Zeeman interaction

This work presents a study of the Faraday instability in a parametrically forced Fermi-Fermi mixture. The condensate is confined in the transversal spatial dimension with a strong parametric confinement potential and in the longitudinal spatial dimension with a weaker potential. The theoretical description is done using the mean-field theory with two amplitude equations that represent each spin state. In order to stabilize the Faraday patterns, a phenomenological damping term is introduced. The influence of the Zeeman interaction is analyzed in detail. In particular, phase diagrams of the existence and stability of the Faraday waves are calculated as a function of the Zeeman interaction, the coupling parameter, and the forcing amplitude. The degree of segregation of the two fields and their synchronization level is also calculated as a function of the Zeeman parameter. In addition, we examine how the pattern wavelength varies as a function of the Zeeman parameter and the forcing frequency.

Density-based turbulence damping at large-scale interface for Reynolds-averaged two-fluid models

The overestimation of turbulence near large-scale interfaces in Reynolds-averaged per-phase turbulence models is a well-known problem. Herein, this is addressed by analyzing the turbulence transport equations and identifying the intrinsic limitation in the formulation of per-phase turbulence models for stratified flow. A novel density-based turbulence damping approach is proposed and compared to a conventional phenomenological damping model and a mixture model for pressurized co- and counter-current as well as gravity-driven stratified air-water flows. The novel approach performs well for all test cases. It is shown that the turbulence damping in the less dense phase is more important than that towards the denser phase. The density-based damping approach leads to more realistic turbulent kinetic energy profiles across the interface region compared to typical existing phenomenological damping approaches. Further, the novel approach does not rely on calibration parameters nor interface indicator functions and is thus well suited for further development of per-phase generalized models.

WITHDRAWN: Density-based turbulence damping at large-scale interface for Reynolds-averaged two-fluid models

Abstract The overestimation of turbulence near large-scale interfaces in Reynolds-averaged per-phase turbulence models is a well-known problem. Herein, this is addressed by analyzing the turbulence transport equations and identifying the intrinsic limitation in the formulation of per-phase turbulence models for stratified flow. A novel density-based turbulence damping approach is proposed and compared to a conventional phenomenological damping model and a mixture model for pressurized co- and counter-current as well as gravity-driven stratified air-water flows. The novel approach performs well for all test cases. It is shown that the turbulence damping in the less dense phase is more important than that towards the denser phase. The density-based damping approach leads to more realistic turbulent kinetic energy profiles across the interface region compared to typical existing phenomenological damping approaches. Further, the novel approach does not rely on calibration parameters nor interface indicator functions and is thus well suited for further development of per-phase generalized models.

Magnon-polaritons in ferromagnetic magnonic crystals with graphene at the interfaces

We present a theoretical study for the surface and bulk magnon-polaritons in magnonic crystals (or semi-infinite layered superlattices), which are formed from an array of ferromagnetic materials and nonmagnetic spacers with graphene sheets interposed between them. The external medium is taken to be vacuum. The Fermi energies in the graphene can be varied by employing different electronic doping levels, resulting in a strong influence exerted by the presence of graphene on the surface magnon-polariton modes. These effects include localization of the modes and control of the group velocities of the modes as the Fermi energies of the graphene sheets are varied, along with an important role for the phenomenological damping in the graphene sheets.

Damped point-vortex model for polar-core spin vortices in a ferromagnetic spin-1 Bose-Einstein condensate

Ferromagnetic spin-1 Bose-Einstein condensates in the broken-axisymmetric phase support polar-core spin vortices (PCVs), which are intimately linked to the nonequilibrium dynamics of the system. For a purely transversely magnetized system, the Turner point-vortex model predicts that PCVs behave like massive charged particles interacting via a two-dimensional Coulomb potential. We test the accuracy of the Turner model for two oppositely charged PCVs, via comparisons with numerical simulations. While the bare Turner model shows discrepancies with our numerical results, we find that a simple rescaling of the PCV mass gives much better agreement. This can be explained via a phenomenological damping arising from coupling to modes extrinsic to the point-vortex phase space. We also identify the excitations produced following PCV annihilation, which help elucidate recent phase ordering results. We extend the Turner model to cases where the system is magnetized both transversally and axially, identifying a crossover to scalar vortex dynamics for increasing external Zeeman field.

Spin-lattice dynamics model with angular momentum transfer for canonical and microcanonical ensembles

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular momentum between the lattice and the spin systems is achieved by a coupling term based upon the spin-orbit interaction. The characteristic spectra of the spin and phonon systems are analyzed for different coupling strength and temperatures. The spin spectral density shows magnon modes together with the uncorrelated noise induced by the coupling to the lattice. The effective damping parameter is investigated showing an increase with both coupling strength and temperature. The model paves the way to understanding magnetic relaxation processes beyond the phenomenological approach of the Gilbert damping and the dynamics of the energy transfer between lattice and spins.

Amplitude modulation and demodulation of a coherent electromagnetic wave in magnetized doped III-V semiconductors

This present paper is concerned with the analytical study of the amplitude modulation and demodulation of a coherent electromagnetic wave in magnetized doped III-V semiconductors. Utilizing the hydrodynamic model of a semiconductor plasma, the modulation indices for upper (+) and lower (–) side bands have been obtained. The incorporation of carrier diffusion in the nonlinear laser-semiconductor interaction adds new dimension to the analysis. The numerical estimations have been made for n-InSb crystal at liquid nitrogen temperature illuminated by frequency doubled pulsed 10.6 µm CO 2 laser. The problem has been analyzed in two different wave regimes (in the presence as well as absence of phenomenological acoustic damping parameter (Γ a ) over a wide range of externally applied magnetic field (incorporated in terms of cyclotron frequency ω c ). The results indicate that in absence of damping parameter, the absorption of coherent electromagnetic radiation takes place completely in all possible wavelength regimes when ω c ~ (v 2 + ω ) 1/2 ; v and ω 0 being the electron collision frequency and pump frequency, respectively. Moreover, the carrier diffusion modifies amplitude modulation and demodulation processes significantly. The damping parameter additionally assumes a significant role in choosing the range of parameters and selecting the modulated side band mode.

Information entropy and population inversion of a three-level semiconductor quantum dot

In this paper, an analytical solution for a three-level semiconductor quantum dot has been presented. From this solution, we have discussed the effects of the phenomenological damping parameters, the electromagnetic field amplitude $$E_{0}$$ of the excitation pulse $$E(\omega )$$ , and the detuning parameters on the atomic occupation probabilities, the atomic population inversion, the purity, and the information entropy $$H(\sigma _\mathrm{{z}}). $$ A long-lived quantum coherence obviously has emerged in all figures. Besides, a decay has appeared in all curves of the atomic occupation probability $$\rho _{gg}(t),$$ the atomic population inversion, and the purity. Since there are not sufficient mathematical solutions for such systems, our study may add further insight into many dynamic systems, and this in turn should open up a wide range of applications for semiconductor quantum dot.

Thermal collapse of a skyrmion

Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice has been investigated. The method is based upon solution of the system of stochastic Landau-Lifshitz equations for up to 104 spins. The recently developed pulse-noise algorithm has been used for the stochastic component of the equations. The collapse rate follows the Arrhenius law. Analytical formulas derived within a continuous spin-field model support numerically-obtained values of the energy barrier. The pre-exponential factor is independent of the phenomenological damping constant that implies that the skyrmion is overcoming the energy barrier due to the energy exchange with the rest of the spin system. Our findings agree with experiments, as well as with recent numerical results obtained by other methods.

Langevin approach to lattice dynamics in a charge-ordered polaronic system

We use a Langevin approach to treat the finite temperature dynamics of displacement variables in the half-filled spinless Holstein model. Working in the adiabatic regime we exploit the smallness of the adiabatic parameter to simplify the memory effects and estimate displacement costs from an "instantaneous" electronic Hamiltonian. We use a phenomenological damping rate, and uncorrelated thermal noise. The low temperature state has checkerboard charge order (CO) and the Langevin scheme generates equilibrium thermodynamic properties that accurately match Monte Carlo results. It additionally yields the dynamical structure factor, $D({\bf q}, \omega)$, from the displacement field $x({\bf r}, t)$. We observe four regimes with increasing temperature, $T$, classified in relation to the charge ordering temperature, $T_c$, and the `polaron formation' temperature $T_P$, with $ T_c \ll T_P$. For $T \ll T_c$ the oscillations are harmonic, leading to dispersive phonons, with increasing $T$ bringing in anharmonic, momentum dependent, corrections. For $T \sim T_c$, thermal tunneling events of the $x({\bf r})$ field occur, with a propagating `domain' pattern at wavevector ${\bf q} \sim (\pi, \pi)$ and low energy weight in $D({\bf q}, \omega)$. When $T_c < T < T_P$, the disordered polaron regime, domain structures vanish, the dispersion narrows, and low energy weight is lost. For $T \gtrsim T_P$ we essentially have uncorrelated local oscillations. We propose simple models to analyse this rich dynamics.

Influence of the magnon–phonon relaxation in the magnon transport under thermal gradient in yttrium iron garnet

We investigate the influence of the magnon–phonon relaxation processes in the magnon transport under thermal gradient in the ferrimagnetic insulator yttrium iron garnet (YIG). Based on the Boltzmann equation we calculate the magnon contribution in the thermal conductivity in YIG and the longitudinal spin Seebeck effect in YIG/Pt films, including the influence of the magnon relaxation to the lattice through a phenomenological damping parameter. Our results are in good agreement with reported experimental data showing that besides the magnon–magnon relaxation processes, the magnon–phonon relaxation plays an important role in the thermal properties in YIG films.

Comparative study of methodologies to compute the intrinsic Gilbert damping: interrelations, validity and physical consequences

Relaxation effects are of primary importance in the description of magnetic excitations, leading to a myriad of methods addressing the phenomenological damping parameters. In this work, we consider several well-established forms of calculating the intrinsic Gilbert damping within a unified theoretical framework, mapping out their connections and the approximations required to derive each formula. This scheme enables a direct comparison of the different methods on the same footing and a consistent evaluation of their range of validity. Most methods lead to very similar results for the bulk ferromagnets Fe, Co and Ni, due to the low spin–orbit interaction (SOI) strength and the absence of the spin pumping mechanism. The effects of inhomogeneities, temperature and other sources of finite electronic lifetime are often accounted for by an empirical broadening of the electronic energy levels. We show that the contribution to the damping introduced by this broadening is additive, and so can be extracted by comparing the results of the calculations performed with and without SOI. Starting from simulated ferromagnetic resonance spectra based on the underlying electronic structure, we unambiguously demonstrate that the damping parameter obtained within the constant broadening approximation diverges for three-dimensional bulk magnets in the clean limit, while it remains finite for monolayers. Our work puts into perspective the several methods available to describe and compute the Gilbert damping, building a solid foundation for future investigations of magnetic relaxation effects in any kind of material.

Josephson flux-flow oscillator: The microscopic tunneling approach

We elaborate a theoretical description of large Josephson junctions which is based on the Werthamer's microscopic tunneling theory. The model naturally incorporates coupling of electromagnetic radiation to the tunnel currents and, therefore, is particularly suitable for description of the self-coupling effect in Josephson junction. In our numerical calculations we treat the arising integro-differential equation, which describes temporal evolution of the superconducting phase difference coupled to the electromagnetic field, by the Odintsov-Semenov-Zorin algorithm. This allows us to avoid evaluation of the time integrals at each time step while taking into account all the memory effects. To validate the obtained microscopic model of large Josephson junction we focus our attention on the Josephson flux flow oscillator. The proposed microscopic model of flux flow oscillator does not involve the phenomenological damping parameter, rather, the damping is taken into account naturally in the tunnel current amplitudes calculated at a given temperature. The theoretically calculated current-voltage characteristics is compared to our experimental results obtained for a set of fabricated flux flow oscillators of different lengths. Our theoretical calculation agrees well with the obtained experimental results, and, to our knowledge, is the first where theoretical description of Josephson flux flow oscillator is brought beyond the perturbed sine-Gordon equation.

Effects of electronic relaxation processes on vibrational linewidths of adsorbates on surfaces: The case of CO/Cu(100)

We investigate nonadiabatic effects for the vibrational stretch mode of the CO molecule adsorbed on the top site of the Cu(100) surface. By studying the long-wavelength ($\mathbf{q}\ensuremath{\approx}0$) imaginary and real parts of the density functional theory based phonon self-energy due to the electron-phonon coupling ${\mathrm{\ensuremath{\Pi}}}_{\ensuremath{\lambda}}$ we obtain the phonon linewidth and the frequency renormalization of the CO stretch mode, respectively. To simulate electronic scattering processes that lead to further damping of the phonon modes we include a phenomenological damping in the phonon self-energy, as well as in the single-electron spectral function that enters ${\mathrm{\ensuremath{\Pi}}}_{\ensuremath{\lambda}}$, through the momentum distribution function. For the specific case of electron-impurity scattering we explicitly show how this process opens the indirect intraband channel and broadens the linewidth of the CO stretch mode. To emphasize the importance of accounting for electronic scattering processes we compare the phonon linewidths in the clean noninteracting limit (infinite electron lifetime) and when electronic scattering processes are phenomenologically included (finite electron lifetime) with available experimental data. We find that the agreement with experiments is improved in the latter case.